Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Boole, Shannon, and Probability
View through CrossRef
George Boole and Claude Shannon shared a deep interest in the mathematics of probability. Boole's interest was, of course, not related to the theory of computation—he was a century too early for that—while Shannon's mathematical theory of communication and information processing is replete with probabilistic analyses. There is, nevertheless, an important intersection between what the two men did, which is shown in this chapter. The aim is to provide a flavor of how they reasoned and of the sort of probabilistic problem that caught their attention. Once we have finished with Boole's problem, the reader will see that it uses mathematics that will play a crucial role in answering Shannon's concern about “crummy” relays.
Title: Boole, Shannon, and Probability
Description:
George Boole and Claude Shannon shared a deep interest in the mathematics of probability.
Boole's interest was, of course, not related to the theory of computation—he was a century too early for that—while Shannon's mathematical theory of communication and information processing is replete with probabilistic analyses.
There is, nevertheless, an important intersection between what the two men did, which is shown in this chapter.
The aim is to provide a flavor of how they reasoned and of the sort of probabilistic problem that caught their attention.
Once we have finished with Boole's problem, the reader will see that it uses mathematics that will play a crucial role in answering Shannon's concern about “crummy” relays.
Related Results
Beyond Boole and Shannon
Beyond Boole and Shannon
Boole and Shannon never studied the physics of computation. Obviously Boole simply could not have, as none of the required physics was even known in his day, and Shannon was nearin...
Entropy and Ergodicity of Boole-Type Transformations
Entropy and Ergodicity of Boole-Type Transformations
We review some analytic, measure-theoretic and topological techniques for studying ergodicity and entropy of discrete dynamical systems, with a focus on Boole-type transformations ...
George Boole and Claude Shannon
George Boole and Claude Shannon
This chapter presents brief biographical sketches of George Boole and Claude Shannon. George was born in Lincoln, a town in the north of England, on November 2, 1815. His father Jo...
AI Uncertainty Based on Rademacher Complexity and Shannon Entropy
AI Uncertainty Based on Rademacher Complexity and Shannon Entropy
In this paper from communication channel coding perspective we are able to present both a theoretical and practical discussion of AI’s uncertainty, capacity and evolution for patte...
On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid
On a Generalization of the Jensen–Shannon Divergence and the Jensen–Shannon Centroid
The Jensen–Shannon divergence is a renown bounded symmetrization of the Kullback–Leibler divergence which does not require probability densities to have matching supports. In this ...
Analisis Bibliometrik Shannon Entropy: Tren Penelitian dan Relevansi Multidimensional
Analisis Bibliometrik Shannon Entropy: Tren Penelitian dan Relevansi Multidimensional
Dengan meningkatnya adopsi Shannon Entropy di berbagai bidang, penting untuk melakukan analisis komprehensif mengenai perkembangan penelitiannya, termasuk tren utama, kolaborasi an...
A brief description about the fathers of computer and information sciences
A brief description about the fathers of computer and information sciences
AbstractIn this article, we are mainly presenting a tribute to the fathers of computer and information sciences, George Boole and Claude Elwood Shannon with their hardships and ach...
Inequalities Revisited
Inequalities Revisited
In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class...